oooooo! How exciting! Puzzle solved - many thanks Gadget.
Thanks for your input too Andy. I initially thought that Ellen = Helen, however on the 1881 census Jessie appears to be living with unmarried 36 year old daughter Helen Bell, so I thought that Ellen must be a different daughter. I will investigate this further.
Gadget, I also thought that Jessie = Janet, but she appears to be Jessie her entire life and dies as Jessie in 1881 age 71, indicating a date of birth of approx 1810.

Re the death of James Bell b 1830, parents William Bell collier and Minnie Armstrong. I had these 2 marriages (which I didn't mention in my question as I thought they might complicate matters):
William Bell = Wilhemina Armstrong
1 Jul 1820 Canonbie (IGI
extracted)
or
14 Jul 1820 (IGI
submitted)
AND
William Bell = Margaret Armstrong Mar 1821 Canonbie (IGI
extracted) or
2 Mar 1821 (IGI
submitted)

I looked up "Minnie" here:
http://www.behindthename.com/nm/m4.php and it says Minnie = Wilhelmina. The William Bell marriage to Wilhelmina stood out like a sore thumb due to one of William's daughters being called Wilhelmina ... but he also has a daughter Margaret (though with Jessie), so i was a bit befuddled. So that clears that up nicely.

And now we know that Jessie Brown was married to John Elliot -

Wonderful.
Off on a slight tangent here ... As our Scottish Jessie Brown/Elliot/Bell thoughtlessly died in Carlisle England in 1881, and her death certificate will not give us the information we need, is there any other way that we can discover who her parents were?
Thanks ever so much for solving my puzzle Gadget. Your time and trouble is very much appreciated. I am working with one of William and Jessie's descendants on this line and she was so confused she has put them aside for a while. She will be thrilled that we now have an answer.
